What does the semicolon at the end of Acts 3:19 indicate?
It indicates the sentence and thought continue into Acts 3:20, not end at verse 19. Israel's repentance and conversion connect with the times of refreshing and God sending Jesus Christ, whose remaining purpose is to be King. So the semicolon ties the promised refreshing to the Messiah's return as King.
Les teaches that the semicolon at the end of Acts 3:19 is significant because it is not a period. The thought continues into verse 20: after Israel is converted and the times of refreshing come from the presence of the Lord, God will send Jesus Christ. Les points out that Christ has already fulfilled the work of the cross, so the only purpose left is for Him to return as King. This connects Israel's repentance and conversion with the promised times of refreshing and the sending of the Messiah-King, rather than ending the sentence at verse 19.